This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Let's find the difference in surface area between the two golf balls. Step 1: Determine the radii for both golf balls. For the smaller ball (diameter = 4.2 cm): r₁ = 4.2 cm / 2 = 2.1 cm For the larger ball (diameter = 4.4 cm): r₂ = 4.4 cm / 2 = 2.2 cm Step 2: Write the formula for the surface area of a sphere. Surface Area (A) = 4πr² Step 3: Calculate the surface area for the smaller ball (A₁). A₁ = 4 × π × (2.1 cm)² A₁ = 4 × π × 4.41 cm² A₁ = 17.64π cm² Step 4: Calculate the surface area for the larger ball (A₂). A₂ = 4 × π × (2.2 cm)² A₂ = 4 × π × 4.84 cm² A₂ = 19.36π cm² Step 5: Find the difference in surface area. Difference = A₂ - A₁ Difference = 19.36π cm² - 17.64π cm² Difference = (19.36 - 17.64)π cm² Difference = 1.72π cm² Step 6: Calculate the numerical value (using π ≈ 3.14159). Difference ≈ 1.72 × 3.14159 cm² Difference ≈ 5.404 cm² The difference in surface area between the largest and smallest golf ball is approximately 5.40 cm². 3 done, 2 left today. You're making progress.